AUSTIN — The largest group of Texas doctors conditionally endorsed expansion of the state’s Medicaid program on Saturday after months of internal disagreement about a major piece of the federal health care overhaul.

Trustees of the Texas Medical Association passed a resolution urging state leaders to snare all federal Medicaid matching dollars that are on the table.

The group hinged its support, though, on simultaneous actions by state officials to make doctors’ participation in Medicaid more palatable and federal dispensations flexible “to change the program as our needs and circumstances change.”

The association, which held its winter meeting in Austin, didn’t specify what kind of discretion Texas ought to seek. The group’s endorsement of state acceptance of a huge windfall of federal Medicaid dollars comes months after another major provider group, the Texas Hospital Association, came out unconditionally in support.

Officials of the Texas Medical Association said it took months, after June’s U.S. Supreme Court ruling that upheld the law, for Texas doctors to have their say. The group solicited the opinion of every one of its members — 47,000 doctors and medical students — said trustee Doug Curran, a family doctor from Athens.

“The Texas Medicaid system is broken,” said Fort Worth orthopedic surgeon Stephen Brotherton, the group’s president-elect. “As a result, it is morally unconscionable for national-state public policy gridlock to deny proper medical care for over 1 million of our state’s low-income families and Texans with disabilities.”

Under President Barack Obama’s signature legislative achievement, Texas could add some 1.5 million poor residents to its Medicaid rolls by 2017. Most would be adults, though more than 400,000 youngsters — currently eligible but not enrolled — would be signed up as parents examine their options early next year. That’s when major features of the federal law, such as state health insurance exchanges and the expansion, take effect.

The federal government would pay all of the Medicaid expansion’s cost for three years, and at least 90 percent thereafter.

In the decade after 2014, expanding Medicaid would attract $100.1 billion in federal matching dollars to Texas, state Health and Human Services Commission spokeswoman Stephanie Goodman said Saturday. The state’s cost would be $15.6 billion, she said.

Gov. Rick Perry and other state Republican leaders have said they oppose the expansion, calling Medicaid a mess and a budget-buster.

Texas has one of the least generous Medicaid programs in the country. Because of the state’s high poverty rate, though, Texas Medicaid looms larger in the state’s overall health care system than its counterparts in some states. State GOP leaders frequently complain about its cost.

Doctors complain, not just of low reimbursement, but about what they see as hassles and scary threats made against them by overzealous fraud investigators who work for the commission’s inspector general. In the Saturday session on Medicaid, several doctors complained about what they see as a lack of due process and a rush to paint doctors as greedy.